1. Field
This application relates to methods of characterizing earth formations by combining and analyzing data from many sources. The sources are the responses to different geometrical and physical properties of the reservoir or different combinations thereof. This application more particularly relates to methods of characterizing formations by utilizing a combination of measurements of different formation exploration tools via a compact inversion parameter set that make use of underlying laws of motion, rules of thermodynamics, and principles related to responses from stimuli.
2. State of the Art
The ability to simulate the movement of the fluid injected into a formation and to predict the movement of multiple phases and the components therein is useful both in the process of producing hydrocarbons from a formation and in the process of quantifying the capacity and containment of underground storage of CO2. For reservoir characterization, owing to spatial sparsity of data, geostatistical methods that propagate near well-bore information or outcrop variograms are usually employed. But by the very nature of the approach, the statistics are based on limited information, use few physical constraints, and are themselves prone to error. Essentially, data are created. To a large extent, the consequential lack of reservoir performance predictability is common to CO2 sequestration and oil and gas production.
For reservoir flow prediction, in addition to near well-bore uncertainty, inter-well properties are obtained through interpolation or geostatistics, but these have large error. It is often thought that with monitoring wells, and with multiple modes of monitoring, a better understanding of the reservoir is possible. Multi-well data, while useful, provides supplementary fluid movement data. But the same problems encountered in single-well data persist. Each of the multiple stimuli induces its own response, and at best only partial consistency is imposed. Furthermore, the presence of a monitoring well-bore and the completions within it affect the very displacement that one is interested in quantifying. Thus, any inference from a near well-bore measurement must account for the altered displacement and/or property profiles, which presents a difficult task. For all of the above-mentioned reasons, inversion remains ill-posed. Indeed, the inability to enforce consistency between inversions of response to one stimulus with another is problematic in reservoir flow characterization. Given the complexity of natural porous materials, it is unrealistic to expect universality of petrophysical relationships.
One problem in reservoir characterization is the lack of spatially distributed data. Another problem is that the data are often indirect, and so are responses, each one of which being governed by its own physics that dictates cause and effect relationship. As an example, consider displacement of one fluid by another in a porous medium. Replacement causes a change in saturation. Assuming that the displacing fluid is non-conductive, and has a neutron capture cross-section different from that of the displaced fluid, and further assuming that the displacing and the displaced fluids are immiscible, the displacement process then alters the behavior of the reservoir to a stimulus that involves current injection, or, neutron pulses. When the densities are different, the gravitational attraction will also change, and the acoustic responses will likely also be altered due to effective compressional and shear velocity changes. During displacement, saturation changes also alter overall hydraulic resistance to flow due to relative permeability and viscosity changes. Therefore, the pressure response for a fixed flow rate would change.
Traditional interpretation methods essentially treat each type of data on its own merit. Well-test analysis infers permeability, skin, and flow barriers from pressure data. Inter-well electromagnetic data is used to invert for resistivity pixels or voxels. Change in the acceleration due to gravity with respect to z or the vertical height, may be similarly utilized to get a coarse distribution of densities. As a result, a poorly resolved density distribution is obtained without concern for physical plausibility with respect to displacement physics or the relevant thermodynamics. The consequence of such disparate approaches is that regularized inversion of apparently independent data may violate the laws governing motion of fluids. For example, tomographic inversion of gravity data may lead to a heavier fluid placed above a lighter fluid without regard to Rayleigh-Taylor instability.
More recently, some work has been done in attempting to account for and reconcile different types of data during analysis of a formation to as to avoid unacceptable solutions. For example, in Ramakrishnan, T. S. and Wilkinson, D., Formation Producibility and Fractional Flow Curves from Radial Resistivity Variation Caused by Drilling Fluid Invasion. Phys. Fluids 9(4), 833-844 (1997), and in Ramakrishnan, T. S. and Wilkinson, D., Water-Cut and Fractional-Flow Logs from Array Induction Measurements. SPE Reservoir Eval. Eng. 2 (1), 85-94 (1999) the concept of inverting electrical responses directly in terms of the underlying multiphase flow properties was proposed. A multicomponent-multiphase fluid mechanics model was used, which when combined with a petrophysical relation allowed for the computation of a conductivity profile. With the tool characteristic response to a conductivity profile included in the forward predictive calculations, comparison with the data obtained within a wellbore was possible. By inverting the measured conductivity responses in terms of a fluid mechanically relevant parameter set, quantities also relevant to future flow performance were obtained. In contrast to continuous logging, on a formation interval length scale, U.S. Pat. No. 6,061,634 to Belani, et al., proposed combining pressure measurements with electrical responses so that a flow model based inversion could be carried out. Sharpness in the inverted results, as imposed by the transport model originating from fluid mechanical considerations could be obtained.
It is also known to allow for current injection through a series of electrodes, with voltages measured simultaneously. The electrodes thus function as both a current source and a voltage pick-up. The actual field deployment and measurement in such an arrangement was illustrated by Kuchuk, et al., Determination of In Situ Two-Phase Flow Properties Through Downhole Fluid Movement Monitoring, SPE. Res. Eval. Eng. 13 (4), 575-587 (2010), and Zhan, et al., Characterization of Reservoir Heterogeneity Through Fluid Movement Monitoring With Deep Electromagnetic and Pressure Measurements, SPE Res. Eval. Eng. 13, 509-522 (2010) where pressure-flowrate/voltage-current responses were inverted.
The integration of a multitude of data types for understanding anomalous responses in carbonate formations was described in U.S. Pat. No. 6,088,656 to Ramakrishnan et al., and in Ramakrishnan et al., A Petrophysical and Petrographic Study of Carbonate Cores from the Thamama Formation, 8th Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE, SPE49502 (1998), as well as Ramakrishnan et al., A Model-Based Interpretation Methodology for Evaluation Carbonate Reservoirs, SPE Annual Technical Conference and Exhibition, SPE71704 (2001). Unlike sandstones, these responses were caused largely by microscopic heterogeneity. These references combined largely diverse responses in a somewhat sequential fashion in order to infer a few parameters related to the underlying pore arrangements such as inter- and intra-granular pore fractions, their length scales and vug fraction. These parameters applied to a matrix surrounded by previously identified fractures. With these, an attempt was made to invert for fractional flow behavior with the approach as given by previously referenced Ramakrishnan, T. S. and Wilkinson, D. (1999). This approach is only partially consistent given that the latter work assumes the pore structure to be unimodal for computing relative permeability functions. The sequential approach also assumed that the nuclear logs are largely processable without having a large sensitivity to multiple liquid phases; but mineralogy contributions are taken into account since they have a measurable impact on density and neutron responses.
The past work of partly sequential steps was tailored towards near wellbore logging in an oil-water environment where a fully integrated simultaneous inversion could be circumvented. Nuclear logs were processed first to infer mineralogy and porosity without having to account for filtrate invasion. Acoustic interpretation that is insensitive to pore fluid, e.g. shear modulus, was used to infer components of porosity. Very shallow logs (e.g. NMR, FMI) were presumed to be obtained in a fully invaded zone. Once pororsity components and pore sizes were inferred, resistivity interpretation was carried out using an invasion model. The separation of logs into those affected by fluids, and those that are not, and those that are sufficiently shallow that the underlying saturation distribution is unambiguously determined, works robustly for near wellbore interpretation. But this is not sufficiently general for deeper measurements. It is also ineffective in dealing with media where heterogeneities affect the measurements, and large scale structural or strata needs to be considered during inversion.
Integration of measurements by classifying them into near wellbore and deep reading data while satisfactory for many purposes, fails as a general purpose method because it does not honor all of the response characteristics associated with each measurement. Although historical work carried out an integration by characterizing pore geometry, the past work did not take into consideration the response behavior for each of the tools, and in particular did not consider gravity, capillarity and the multidimensionality of the displacement processes. Each depth was treated in its own merit, i.e., two and three dimensional effects on log responses went unaccounted.
More recent work has been proposed to integrate electromagnetic and seismic measurements by having a common porosity and saturation model. See, Gao, G. et al., Joint Inversion of Cross-well Electromagnetic and Seismic Data for Reservoir Petrophysical Parameters, SPE 135057 (2010). These models are based on commercially available numerical reservoir simulators that fail to capture wellbore and near boundary related near wellbore behavior correctly, and do not account for response relevant property variations relevant to responses in a thermodynamically consistent fashion.